Gamma exposure and risk management

With very strict limits on the delta exposure that the trading desks are permitted, most profit/losses that the desk realizes is explained by changes in equity volatility, gamma PnL, changes in equity correlations markings, FX vols, Equity FX correlations, interest rates, repo rates and expected dividends. Ocassionally windfalls [applicable to overhedges] also contribute to the PnL. The trading strategies of the desks to a large extent center around the gamma and the volatility exposures based on the market view they have. In this article we shall try to understand the gamma risks.

While being long gamma requires funding costs (i.e requires investment to buy options), being short gamma earns that investment money. So by being long gamma you would realize negative PnL on theta whereas positive PnL on theta by being short gamma [well almost always - one exception being long deep ITM puts are long theta]. One common practise is to be long gamma in trending markets and short gamma for ranged bound (or sluggish) markets.

In the discussion that follows we assume that the portfolio is delta hedged at discrete intervals. Of course if we keep the portfolfolio continuously delta hedged, we would not realized any PnL [the argument assumes that the other risk factors do not change] i.e the realized PnL is due to the deltas accumulated between the rehedgings. It will be worth noticing in the discussion that follows how the perspectives of the risk managers and traders sometimes (may be often) differ.

Lets take the first scenario, the market is rallying (stocks moving up). The traders would like to have long gamma exposures in such a market. With a long gamma exposure, as the markets rally the portfolio picks up more delta between rehedgings. To keep the portfolio delta hedged as the market moves up and the portfolio picks up positive delta, the trader will sell the stocks [or forwards]. With markets going up the trader is selling at a high [sell at a high while have bought at a low] thus making profits. When the trader expects that the market will continue to rally, he would delta hedge less often to be able to accumulate more deltas [and hence more profits].

In another situation we suppose that the markets were crashing, the trader would again like a long gamma exposure. The portfolio would be picking up negative delta which the trader would cover by buying stocks [buying low] in a falling market. The trader is making a profit in this situation by accumulating negative deltas on the way down.

It would start to appear that being long gamma always gives you a profit. Well umm.. not always. Remember that we told that positive gamma is an expensive strategy because of the time decay. To be able to earn profits overall, the stock movements should be able to compensate for the loss in time decay. So when the trader believes that the market is going to be sluggish [small moves], he would keep a short gamma position and be happy to earn PnL due to theta. But, being short gamma is a risky strategy. The trader will start loosing money in trending markets. The analysis is similar to the discussion above, when the market crashes the portfolio picks up positive delta and the trader will find himself in a situation where he is selling when the market is crashing [selling low]. Similarly when the market rallies, the portfolio would pick up negative delta and the trader would find himself in a situation where he's buying in the peaking market to delta hedge. In a collapsing market the traders sometimes might like to hedge less often in the hope that the market would rebound [after all you dont realize profit or loose unless you book it]. But then the risk manager should know that this strategy runs the risk of realizing even more losses in future by not booking small ones today. Hence short gammas can get the risk managers worried.